TEFL: Prediction-Residual-Guided Rolling Forecasting for Multi-Horizon Time Series

Authors: Xiannan Huang, Shen Fang, Shuhan Qiu, Chengcheng Yu, Jiayuan Du, Chao Yang Date: 2026-02-26 Paper ID: openalex:2602.22520

Summary

This paper introduces Temporal Error Feedback Learning (TEFL), a novel framework designed to enhance deep multi-horizon time series forecasting by explicitly utilizing historical prediction residuals generated during rolling evaluation. TEFL addresses the partial observability of residuals in multi-step settings by selecting observable errors and integrating them via an efficient, lightweight low-rank adapter to prevent overfitting. The method employs a two-stage training procedure to jointly optimize the base forecasting model and the error feedback module. Extensive experiments demonstrate that TEFL provides a general and effective enhancement, yielding consistent accuracy gains (5-10% MAE reduction) and superior robustness against distribution shifts compared to standard point-wise loss minimization training.

Key Contributions

• Proposed TEFL, a unified framework that explicitly incorporates historical prediction residuals from rolling forecasts into deep forecasting models.
• Addressed challenges of selecting observable multi-step residuals and integrating them via a lightweight low-rank adapter for efficiency.
• Designed a two-stage training procedure that jointly optimizes the base forecaster and the error feedback module.
• Achieved consistent accuracy improvements (5-10% average MAE reduction) across 5 backbone architectures and 10 datasets, demonstrating strong robustness to distribution shifts.

Limitations

The paper focuses on improving accuracy via residual feedback; further exploration into why specific residuals correlate with future error could lead to more theoretically grounded improvements.

Open Questions & Future Work

• tefl-extension-to-online-learning

Key Concepts

• Temporal Error Feedback Learning: A unified framework that explicitly incorporates historical prediction residuals from rolling forecasts into the deep time series forecasting pipeline during both training and evaluation.

Datasets

• 10 real-world datasets

Limitations

The paper focuses on improving accuracy via residual feedback; further exploration into why specific residuals correlate with future error could lead to more theoretically grounded improvements.

Links

• Abstract
• PDF